Question 61685
Find the equation of the line through (2,4) which is perpendicular
to the line {{{y = x}}}
The slope of {{{y = x}}} is +1
A line perpendicular to it will have slope = -1
{{{y = mx + b}}}
{{{y = -x + b}}}
It goes through (2,4)
{{{4 = -2 + b}}}
{{{b = 6}}}
{{{y = -x + 6}}} is the equation of AD
Find intersection of {{{y = x}}} and {{{y = -x + 6}}}
add the equations
{{{2y = 6}}}
{{{y = 3}}}
{{{x = 3}}} also
(3,3) is the point D
To get the area of the square, find length AD and square it
{{{(x[a] - x[d])^2 + (y[a] - y[d])^2  = l^2}}}
note that {{{l^2}}} is the area
{{{(2 - 3)^2 + (4 - 3)^2 = A}}}
{{{(-1)^2 + 1^2 = A}}}
{{{A = 1 + 1}}}
{{{A = 2}}} area abcd